Exact Algorithms for Set Multicover and Multiset Multicover Problems

Hua, Qiang-Sheng; Yu, Dongxiao; Lau, Francis C. M.; Wang, Yuexuan

doi:10.1007/978-3-642-10631-6_6

Cited by 26 publications

(24 citation statements)

References 11 publications

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“…As mentioned above, the weighted t-cover hitting set problem is NP-hard and the previous best algorithm for the unweighted case of the problem has a time complexity of O((t + 1) n nm) [4]. In terms of our application, n is the number of co-regulated genes and m is the number of TFs; there two numbers are usually large enough to render the existing algorithms impractical for our problem.…”

Section: Finding Cooperative Tfs For a Set Of Coregulated Genesmentioning

confidence: 98%

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A graph model and an exact algorithm for finding transcription factor modules

2011

Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine

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Systematically perturbing a cellular system and monitoring the effects of the perturbations on gene expression provide a powerful approach to study signal transduction in gene expression systems. A critical step of revealing a signal transduction pathway regulating gene expression is to identify transcription factors transmitting signals in the system. In this paper, we address the task of identifying modules of cooperative transcription factors based on results derived from systems-biology experiments at two levels: First, a graph algorithm is developed to identify a minimum set of co-operative TFs that covers the differentially expressed genes under each systematic perturbation. Second, using a clique-finding approach, modules of TFs that tend to consistently cooperate together under various perturbations are further identified. Our results indicate that this approach is capable of identifying many known TF modules at both the individual experiment level and at the systems level; thus we provide a novel graph-based method of identifying contextspecific and highly reused TF-modules.

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Section: Finding Cooperative Tfs For a Set Of Coregulated Genesmentioning

confidence: 98%

“…The problem of finding the t-TF cover is NP-hard, where the problem is equivalent to two well-known NP-hard problems, the set multicover problem and the t-cover hitting set problem [1,4]. The t-TF cover problem can be reduced to the t-cover hitting set problem easily.…”

Section: Finding Cooperative Tfs For a Set Of Coregulated Genesmentioning

confidence: 99%

A graph model and an exact algorithm for finding transcription factor modules

2011

Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine

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“…Exact algorithms for the set partition problem in Example 4 and for computing cover polynomial in Example 6 are due to Björklund et al [13,15]. In the conference versions [11,40] of [13] and some other papers [12,32,33,31], exact algorithms using inclusion-exclusion for other partitioning and covering problems are given. The inclusion-exclusion technique is also used to give a faster exact algorithm for computing the permanent of a matrix over rings and finite commutative semirings [20].…”

Section: Notesmentioning

confidence: 99%

Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches

Wang

Hua

et al. 2013

Handbook of Combinatorial Optimization

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Abstract. Exponential algorithms, whose time complexity is O(c n ) for some constant c > 1, are inevitable when exactly solving NP-complete problems unless P = NP. This chapter presents recently emerged combinatorial and algebraic techniques for designing exact exponential time algorithms. The discussed techniques can be used either to derive faster exact exponential algorithms, or to significantly reduce the space requirements while without increasing the running time. For illustration, exact algorithms arising from the use of these techniques for some optimization and counting problems are given.

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“…Here we could only touch upon a small subset of them. For more open problems, please refer to (Hua & Lau, 2006, Hua, 2009& Hua et al, 2009a,2009b.…”

Section: Discussionmentioning

confidence: 99%

“…These problems can be formulated as a set covering problem (Hua & Lau, 2008) or as a set multi-covering problem (Hua et al, 2009a(Hua et al, , 2009b). …”

Section: Discussionmentioning

confidence: 99%

Joint Link Scheduling and Topology Control for Wireless Sensor Networks with SINR Constraints

Hua

Lau

Handbook of Research on Developments and Trends in Wireless Sensor Networks

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This chapter studies the joint link scheduling and topology control problems in wireless sensor networks. Given arbitrarily located sensor nodes on a plane, the task is to schedule all the wireless links (each representing a wireless transmission) between adjacent sensors using a minimum number of timeslots. There are two requirements for these problems: first, all the links must satisfy a certain property, such as that the wireless links form a data gathering tree towards the sink node; second, all the links simultaneously scheduled in the same timeslot must satisfy the SINR constraints. This chapter focuses on various scheduling algorithms for both arbitrarily constructed link topologies and the data gathering tree topology. We also discuss possible research directions.

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Exact Algorithms for Set Multicover and Multiset Multicover Problems

Cited by 26 publications

References 11 publications

A graph model and an exact algorithm for finding transcription factor modules

A graph model and an exact algorithm for finding transcription factor modules

Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches

Joint Link Scheduling and Topology Control for Wireless Sensor Networks with SINR Constraints

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